Answer:
Done
Explanation:
To solve the problem, we can use a Venn diagram to visualize the information provided in the question.
Let's draw three overlapping circles to represent the three groups of people: those who eat fruits, those who eat vegetables, and those who eat cheese.
We know that:
- 37 people eat fruits, so we write "37" in the circle representing fruits.
- 33 people eat vegetables, so we write "33" in the circle representing vegetables.
- 9 people eat both cheese and fruits, so we write "9" in the overlap between the cheese and fruits circles.
- 12 people eat both cheese and vegetables, so we write "12" in the overlap between the cheese and vegetables circles.
- 10 people eat both fruits and vegetables, so we write "10" in the overlap between the fruits and vegetables circles.
- 12 people eat only cheese, so we write "12" in the part of the cheese circle that does not overlap with the other circles.
- 3 people eat all three offerings, so we write "3" in the intersection of all three circles.
Here's what the Venn diagram looks like:
```
Cheese
+----9----+----3----+----12---+
| | Cheese | | |
| Fruits +----6----+--4 | |
| | | | |
+----10---+----3----+----8---+---+
| Vegetables |
+------------+
9 24 15
```
To find out how many people eat cheese, we add up the numbers in the cheese circle: 9 + 3 + 12 = 24. So, 24 people eat cheese.
To find out how many people do not eat any of the offerings, we need to add up the numbers in the regions that are not part of any circle: the region outside of all circles, and the region in the center of the Venn diagram. These regions add up to 9 + 15 = 24. So, 100 - 24 = 76 people do eat at least one of the offerings.